In a medium bowl, cream together butter and sugar. When creamy and smooth, add the egg and vanilla extract. Add the oatmeal mixture to the sugar mixture and mix very well. Place the dough in a tightly closed container in the refrigerator until it is firm, about 1 1/2 hours.

Preheat the oven to 400F. For large cookies, form round balls the size of golf balls from the dough. Grease a cookie sheet and place dough balls on the sheet. Use the back of a fork to push down and flatten the balls. Make sure there is enough space between the cookies so that they can expand without touching the others. Place on the middle oven rack for 10-12 minutes.